%___________________________________________________________________%
%  Grey Wolf Optimizer (GWO) source codes version 1.0               %
%                                                                   %
%  Developed in MATLAB R2011b(7.13)                                 %
%                                                                   %
%  Author and programmer: Seyedali Mirjalili                        %
%                                                                   %
%         e-Mail: ali.mirjalili@gmail.com                           %
%                 seyedali.mirjalili@griffithuni.edu.au             %
%                                                                   %
%       Homepage: http://www.alimirjalili.com                       %
%                                                                   %
%   Main paper: S. Mirjalili, S. M. Mirjalili, A. Lewis             %
%               Grey Wolf Optimizer, Advances in Engineering        %
%               Software , in press,                                %
%               DOI: 10.1016/j.advengsoft.2013.12.007               %
%                                                                   %
%___________________________________________________________________%

% Grey Wolf Optimizer
function [Alpha_score,Alpha_pos,Convergence_curve]=GWO(SearchAgents_no,Max_iter,LB,UB,Dim,F_obj)

% initialize alpha, beta, and delta_pos
Alpha_pos=zeros(1,Dim);
Alpha_score=inf; %change this to -inf for maximization problems

Beta_pos=zeros(1,Dim);
Beta_score=inf; %change this to -inf for maximization problems

Delta_pos=zeros(1,Dim);
Delta_score=inf; %change this to -inf for maximization problems

%Initialize the positions of search agents
Positions=initialization(SearchAgents_no,Dim,UB,LB);

Convergence_curve=zeros(1,Max_iter);

l=0;% Loop counter

% Main loop
while l<Max_iter
    for i=1:size(Positions,1)  
        
       % Return back the search agents that go beyond the boundaries of the search space
        Flag4ub=Positions(i,:)>UB;
        Flag4lb=Positions(i,:)<LB;
        Positions(i,:)=(Positions(i,:).*(~(Flag4ub+Flag4lb)))+UB.*Flag4ub+LB.*Flag4lb;               
        
        % Calculate objective function for each search agent
        fitness=F_obj(Positions(i,:));
        
        % Update Alpha, Beta, and Delta
        if fitness<Alpha_score 
            Alpha_score=fitness; % Update alpha
            Alpha_pos=Positions(i,:);
        end
        
        if fitness>Alpha_score && fitness<Beta_score 
            Beta_score=fitness; % Update beta
            Beta_pos=Positions(i,:);
        end
        
        if fitness>Alpha_score && fitness>Beta_score && fitness<Delta_score 
            Delta_score=fitness; % Update delta
            Delta_pos=Positions(i,:);
        end
    end
    
    
    a=2-l*((2)/Max_iter); % a decreases linearly fron 2 to 0
    
    % Update the Position of search agents including omegas
    for i=1:size(Positions,1)
        for j=1:size(Positions,2)     
                       
            r1=rand(); % r1 is a random number in [0,1]
            r2=rand(); % r2 is a random number in [0,1]
            
            A1=2*a*r1-a; % Equation (3.3)
            C1=2*r2; % Equation (3.4)
            
            D_alpha=abs(C1*Alpha_pos(j)-Positions(i,j)); % Equation (3.5)-part 1
            X1=Alpha_pos(j)-A1*D_alpha; % Equation (3.6)-part 1
                       
            r1=rand();
            r2=rand();
            
            A2=2*a*r1-a; % Equation (3.3)
            C2=2*r2; % Equation (3.4)
            
            D_beta=abs(C2*Beta_pos(j)-Positions(i,j)); % Equation (3.5)-part 2
            X2=Beta_pos(j)-A2*D_beta; % Equation (3.6)-part 2       
            
            r1=rand();
            r2=rand(); 
            
            A3=2*a*r1-a; % Equation (3.3)
            C3=2*r2; % Equation (3.4)
            
            D_delta=abs(C3*Delta_pos(j)-Positions(i,j)); % Equation (3.5)-part 3
            X3=Delta_pos(j)-A3*D_delta; % Equation (3.5)-part 3             
            
            Positions(i,j)=(X1+X2+X3)/3;% Equation (3.7)
            
        end
    end
    l=l+1;    
    Convergence_curve(l)=Alpha_score;
end

%%
function Positions=initialization(SearchAgents_no,dim,ub,lb)

Boundary_no= size(ub,2); % numnber of boundaries

% If the boundaries of all variables are equal and user enter a signle
% number for both ub and lb
if Boundary_no==1
    Positions=rand(SearchAgents_no,dim).*(ub-lb)+lb;
end

% If each variable has a different lb and ub
if Boundary_no>1
    for i=1:dim
        ub_i=ub(i);
        lb_i=lb(i);
        Positions(:,i)=rand(SearchAgents_no,1).*(ub_i-lb_i)+lb_i;
    end
end